A mass is placed on a horizontal, frictionless surface and three forces are appl

Question

A mass is placed on a horizontal, frictionless surface and three forces are applied to it.  F1 has a magnitude of 62 Newtons is directed at an angle of 26 degrees above the positive x axis, F2 has a magnitude of 5 Newtons is directed in the negative y direction, and F3 has a magnitude of 14 Newtons is directed at an angle of 68 degrees below the negative x axis. If the mass is a low enough value such that the mass just begins to leave the surface (just begins to leave… has not left surface), what is the acceleration in the x direction in m/s2?

Explanation / Answer

Here ,

F1 = 62 * (cos(26) i + j * sin(26))

F2 = -5 j

F3 = 16 *(- cos(16) i - j * sin(16) )

Now , for the net force acting on the block

Fnet = F1 + F2 + F3

Fnet = 62 * (cos(26) i + j * sin(26)) - 5 j + 16 *(- cos(16) i - j * sin(16) )

Fnet = 40.4 i + 17.8 j

Now , for the block to just leave the floor ,

mg = 17.8 N

m = 1.813 Kg

let the accelration is a

a = 40.4/1.813

a = 22.3 m/s^2

the acceleration in the x - direction is 22.3 m/s^2

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